The following table shows the number of hours some middle school students in two cities spend texting each week: City A 9 27 17
24 21 12 25 25 18 City B 6 20 26 15 23 25 14 14 11 Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (6 points) Part B: Are the box plots symmetric? Justify your answer. (4 points)
1 answer:
The five-number summary consists of the minimum, maximum, third quartile (Q₃), median (Q₂), and first quartile (Q₁)
. The initial action is to sort each data set in increasing order as demonstrated in the first diagram
. The median (Q₂) for both data sets can be found at the
position.
After identifying the median, we divide the data into two sections: one to the left and one to the right of the median, where Q₁ and Q₃ will be positioned.
Q₁ is found between the
and 
values, while Q₃ lies between the 
and 
values.
The box plots for both data sets appear in the second diagram
. The box plots exhibit asymmetry. City A's box plot stretches more to the left (indicative of negative skew), and City B's box plot also extends leftward (showing negative skew).
. The initial action is to sort each data set in increasing order as demonstrated in the first diagram
. The median (Q₂) for both data sets can be found at the
After identifying the median, we divide the data into two sections: one to the left and one to the right of the median, where Q₁ and Q₃ will be positioned.
Q₁ is found between the
The box plots for both data sets appear in the second diagram
. The box plots exhibit asymmetry. City A's box plot stretches more to the left (indicative of negative skew), and City B's box plot also extends leftward (showing negative skew).
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